On another front, scalar coupled black hole solutions with
different asymptotic spacetime structure is a subject of interest
for a long time. There has been a renewed interest in such studies
ever since new black hole solutions have been found in the context
of string theory. The low energy effective action of string theory
contains two massless scalars namely dilaton and axion. The
dilaton field couples in a nontrivial way to other fields such as
gauge fields and results into interesting solutions for the
background spacetime. It was argued that with the exception of a
pure cosmological constant, no dilaton-de Sitter or anti-de Sitter
black hole solution exists with the presence of only one
Liouville-type dilaton potential [1]}. Recently, the dilaton
potential leading to (anti)-de Sitter-like solutions of dilaton
gravity has been found [2]}. It was shown that the
cosmological constant is coupled to the dilaton in a very
nontrivial way. With the combination of three Liouville-type
dilaton potentials, a class of static dilaton black hole solutions
in (A)dS spaces has been obtained by using a coordinates
transformation which recast the solution in the schwarzschild
coordinates system [2]}. More recently, a class of charged
rotating dilaton black string solutions in four-dimensional
anti-de Sitter spacetime has been found in [4]}. Other
studies on the dilaton black hole solutions in (A)dS spaces have
been carried out in [5]}, [6]}.
